A major constraint to construct models with two Higgs doublets (2HDMs) arises from flavour changing neutral currents, which are typically ubiquitous in these models. Requiring Natural Flavour Conservation (NFC) restricts the models to four different classes which differ by the manner in which the Higgs doublets couple to fermions [1]}, [2]}, [3]}. They are organized via discrete symmetries like \(Z_2\)  under which different matter sectors, such as right-handed leptons or left-handed quarks, have different charge assignments. These models are labeled as type I, II, “lepton-specific" (or X) and “flipped" (or Y). Normalizing the Yukawa couplings of the neutral bosons in such a way that the explicit Yukawa interaction terms in the Lagrangian are given by \((y^{\phi }_f) \frac{m_f}{\upsilon } \bar{f} f \phi \)  for the CP-even scalars \(\phi =h, H\)  (lighter and heavier, respectively) and \(i (y^A_f) \frac{m_f}{\upsilon }\bar{f} \gamma _5 f A\)  for the pseudoscalar \(A\)  in the mass eigenstate basis, the \(y^{h,H,A}_f\)  factors are summarized in Table I for each of these four types of 2HDMs as functions of \(\tan \beta \equiv v_2/v_1\) , the ratio of the two Higgs vacuum expectation values, and the diagonalization angle \(\alpha \)  of the two CP-even Higgs bosons (\(v=\sqrt{v_1^2 + v_2^2}= 246\)  GeV). It should be noted however, that in addition to these models, NFC can also occur in models with alignment, as in Ref. [4]}. In this class of models, more general sets of relations are imposed on the field content using discrete symmetries similar to \(Z_2\) , which still conserve flavour but allow for CP violation. A class of 2HDMs also exists where one of the Higgs doublets does not participate in the dynamics and remains inert [5]}, [6]}. Finally, in the so-called type III models both up and down fermions couple to both Higgs doublets. A detailed analysis of flavour and CP violation in type III models can be found in [7]} and references therein.
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